So you're close on your basic assumption, but far off enough that you'll wind up likely doing yourself some serious harm. Brass (and several other materials, including silver) are what's considered bacteriostatic. That is to say they stop the growth of bacteria, which is in contrast to something like Lysol, which is bactericidal, which is to say they kill bacteria. What this means is that while this spoon won't assist in the growth of bacteria (unlike a piece of say bread would, providing nutrients), it will do nothing to kill the bacteria or spores on the spoon. The last part about spores is of particular interest here.
Spores, unlike numerous live bacterial strains, are not easily killed by stomach acid, saliva, or sometimes even boiling at 100C. These are one of the primary reasons you wash items, as most bacterial cells die on desiccation alone, though a spore will often times persist.
Add all this to the fact that I'm not really sure brass would be the safest material to consume (heavy metal poising, etc), the additional weight, and perhaps foul taste, I would recommend against this course of action.